CN103869700A - Semi-physical platform for satellite executing mechanism online reconstitution and control method - Google Patents

Abstract

The invention discloses a semi-physical platform for satellite executing mechanism online reconstitution and a control method and belongs to the technical field of aerospace. The semi-physical platform comprises a remote control computer, a remote measuring computer, a satellite-borne control computer and a model simulation computer. In the control method, the satellite-borne control computer determines the attitude angle and the angular velocity of a satellite according to an attitude measurement value of a sensor, and solves a control law and a distributive law according to a target control signal to obtain an actual control signal of an executing mechanism; the executing mechanism produces an attitude control moment under the effect of the actual control signal. According to the semi-physical platform for satellite executing mechanism online reconstitution and the control method, the system resources are fully utilized, the control system design is simplified, the system robustness is improved, and the design complexity of a controller is reduced.

Description

Semi physical platform and the control method of satellite executing mechanism on-line reorganization

Technical field

The semi physical platform and the control method that the invention discloses satellite executing mechanism on-line reorganization, belong to aerospace technical field.

Background technology

Attitude control system, as one of subsystem the most complicated in the many subsystems of satellite, plays very crucial effect in satellite control.But because satellite works long hours in complicated space environment, the parts of posture control system easily break down, need to take certain measure to ensure the performance of attitude control system under failure condition.American National aviation NASA (NASA) has first proposed the concept of reconstruct control in nineteen eighty-two, it is to grow up on the basis of traditional control of redundancy theory.Reconstruct control refers in the time that one or more critical components of system break down or lost efficacy, and by changing the structure of system, utilizes spare part or other operation elements to substitute fault element, with the performance of keeping system.For the satellite attitude control system with the configuration of redundancy topworks, the essence of reconstruct control is the method for using hardware redundancy and resolving redundancy, make full use of the functional redundancy of system self inherence, still can complete attitude control task after topworks is broken down.The research of reconstruct control has great importance to security, stability and the viability etc. that improve satellite.

In recent years, lot of domestic and international scholar, for satellite executing mechanism fault, has launched multiple reconstruct control research, and has verified in theory the validity of control strategy by the method for mathematical simulation.But the research of these reconstructing methods is only confined to part of theoretical study, its engineering realizability is seldom verified.The risk of bringing to high investment aerospace industry for reducing new technology, before the practical application of reconstruct control method, is the validity of authentication control method, improves the degree of confidence of emulation, and semi-physical simulation checking is a link must carrying out.

Satellite attitude control system semi-physical simulation platform interknits the mathematical models such as in kind on the star such as sensor and topworks and space environment exactly, reproduce the practical work process of Satellite Attitude Control System, can be applicable to demonstration and the schematic design phase of system.Satellite attitude control system is a system when strong, topworks needs real-time response steering order, output control moment, sensor needs Real-time Collection celestial body attitude information, passing to controller carries out controlled quentity controlled variable and resolves, therefore, need to use real-time semi-physical simulation platform to meet the requirement of its hard real-time.Existing attitude of satellite control semi-physical simulation platform uses Matlab to write application program more, by RTW, Simulink model is compiled to generating code, download to and on target machine, carry out semi-physical simulation, although method is simple, but high to target machine hardware requirement, code portability is poor, and its real-time can not meet the performance requirement of satellite attitude control system in engineering.Therefore, use hard real time operating system and high reliability hardware device, build a high reliability, high real-time, code portability, rich interface, extendible satellite attitude control system on-line reorganization control semi-physical simulation platform, with the engineering realizability of checking reconstruction strategy, to improving troubleshooting capability and the reconstruct level of satellite attitude control system, conscientiously reliability, maintainability and the validity of safeguards system, the span that realization theory is studied engineering application has great importance.

Summary of the invention

Technical matters to be solved by this invention is the deficiency for above-mentioned background technology, and semi physical platform and the control method of satellite executing mechanism on-line reorganization is provided.

The present invention adopts following technical scheme for achieving the above object:

The semi physical platform of satellite executing mechanism on-line reorganization, comprising:

Remote control computer, sends target control signal to spaceborne control computing machine by switch;

Model emulation computing machine, gather the tach signal of topworks, calculate the control moment acting on satellite body, then the theoretical value that draws attitude of satellite angle and angular velocity according to dynamical model, the kinematics model set up, then sends to spaceborne control computing machine by the sensor attitude measured value obtaining according to attitude sensor model;

Spaceborne control computing machine is equipped with vxworks operating system, determine attitude of satellite angle and angular velocity according to attitude measurement value, resolve control law according to control target and obtain target control signal, resolve again the working control signal that law of distribution obtains topworks, topworks produces attitude control moment under the effect of working control signal, and attitude of satellite angle and angular velocity transfer to remote measurement computing machine by switch;

Remote measurement computing machine, for working control signal of Real time dynamic display attitude of satellite angle, angular velocity and topworks etc.

As the further prioritization scheme of described satellite executing mechanism on-line reorganization semi physical platform, use Visual Studio2005 Software for Design remote control computer interface, use Visual Studio2005 software and Satellite Tool Kit software co-design remote measurement computer interface

Remote measurement computing machine uses VS to set up telemetry interface, and connects STK satellite simulation kit by STKX assembly, calls the application program interface function of STKX assembly, realizes the satellite 3-D Visualization Demo of process in orbit.

The control method of satellite executing mechanism on-line reorganization, utilizes the semi physical platform of satellite executing mechanism on-line reorganization as claimed in claim 1 or 2 to obtain attitude of satellite reconstruct control program, specifically comprises the steps:

Steps A, in the time that flywheel is normally worked, utilizes PD control rate u=K _pα+K _dω+ω × J ω draws the working control signal u of flywheel, wherein, and the attitude angle that α, ω are satellite and angular speed, K _pand K _dfor ratio and differential coefficient, J is satellite moment of inertia;

Step B, in the time that a certain axle flywheel of satellite breaks down and have same axle backup flywheel, switches backup flywheel and substitutes fault flywheel, utilizes and intends PD control rate u=K _pα+K _dω+ω × J ω draws backup flywheel working control signal u;

Step C, breaks down at a certain axle flywheel of satellite, while not having coaxially back up flywheel but have the flywheel of redundant configuration, resolves control law, law of distribution obtains each flywheel working control signal under fault:

Step C-1, uses plan PD control law ν=K according to controlling target _pα+K _dω+ω × J ω obtains target control signal ν, and ν is control moment,

Step C-2, installs Matrix C by flywheel and obtains the relational expression of target control signal ν and working control signal u: ν=Cu,

Step C-3, by flywheel fails matrix E, determines control efficiency Matrix C _f: C _f=CE, the relational expression of combining target control signal ν and working control signal u, considers that energetic optimum uses pseudoinverse technique to control distribution, two norms of getting controlled quentity controlled variable u are performance index, are described as: , try to achieve its optimum solution and be: u=D ν=C ⁺ν, D=C ⁺=C ^t(CC ^t) ^-1for the pseudo-inverse matrix of battle array C is installed, required distribution battle array, considers the property taken advantage of fault, provides satellite attitude control system kinetics equation under failure condition: , wherein: J _ωfor Rotary Inertia of Flywheel, Ω is flywheel angular velocity, the inefficacy matrix E=diag{e under failure condition ₁, e ₂, e ₃, e ₄, 0≤e _i≤ 1, i=1,2,3,4, work as e _i=0 o'clock, i flywheel complete failure; Work as e _i=1 o'clock, i flywheel was normal, and system is installed battle array C _f=CE, the distribution battle array that pseudoinverse technique obtains is

, the pseudo-inverse form u of flywheel working control amount _f, u _f=D _fν, obtains law of distribution expression formula:

Step C-4, considers flywheel actual output torque restricted problem, adopts the distribution amendment scheme based on kernel method, and the original allocation result that pseudoinverse technique is obtained is revised, and obtains working control signal;

Step D, breaks down at a certain axle flywheel of satellite, and not coaxial backup flywheel but while magnetic torquer being housed on three principal axis of inertia of satellite resolves control law, law of distribution and obtain the working control signal of other effective flywheel and magnetic torquer:

Step D-1, uses plan PD control law ν=K according to controlling target _pα+K _dω+ω × J ω obtains target control signal v,

Step D-2, according to actuator failure situation, is decomposed into by target control signal ν the controlled quentity controlled variable M that effective flywheel provides _wthe controlled quentity controlled variable M providing with magnetic torquer _m: ν=M _w+ M _m;

Step D-3, obtains according to magnetic torquer principle of work and Geomagnetic Field Model the controlled quentity controlled variable M that magnetic torquer provides _m, then determine by the expression formula of step D-2 the controlled quentity controlled variable M that effective topworks provides _w,

In the time of Y-axis topworks complete failure, the controlled quentity controlled variable that magnetic torquer provides

, the controlled quentity controlled variable that effectively topworks provides

, μ is for describing magnetic dipole ratings and peaked relation, B _x, B _x, B _xfor geomagnetic field component, M _ythe target control amount M obtaining for PD control law is at the component of Y-axis.

The present invention adopts technique scheme, has following beneficial effect: this patent uses control distribution technique by control law and separately design of law of distribution, can make full use of system resource, simplified control system design; Break down while losing efficacy in part topworks, only need to adjust corresponding control allocative decision and need not change control algolithm and just can realize fault dynamic isolation, can make the variation minimum of system, raising system robustness; And export limited in the situation that in topworks, can be directly retrain processing controlling in allocation algorithm, reduced the complexity that controller designs.

Brief description of the drawings

Fig. 1 is the schematic diagram in kind of embodiment Satellite topworks on-line reorganization semi physical platform.

Fig. 2 is the illustrative view of functional configuration of embodiment Satellite topworks on-line reorganization semi physical platform.

Fig. 3 is the process flow diagram of control method in embodiment.

Fig. 4 (a), Fig. 4 (b) are attitude angle, the angular velocity response curve that in embodiment, under flywheel four angle mount mounting meanss, under non-failure conditions, PD controls.

Fig. 5 is the output torque curve map that is assigned to each flywheel in embodiment under flywheel four angle mount mounting meanss under non-failure conditions.

Fig. 6 (a), Fig. 6 (b) are attitude angle, the angular velocity response curve based on pseudoinverse technique under failure condition under flywheel four angle mount mounting meanss in embodiment.

Fig. 7 is the response curve of flywheel output torque of pseudoinverse technique after distributing under failure condition under flywheel four angle mount mounting meanss in embodiment.

Fig. 8 (a), Fig. 8 (b) in embodiment when Y-axis flywheel fault flywheel and magnetic torquer jointly control attitude angle and angular velocity response curve.

Fig. 9 is flywheel output torque response curve when flywheel and magnetic torquer jointly control under Y-axis flywheel fault in embodiment.

Figure 10 is magnetic torquer output torque response curve when flywheel and magnetic torquer jointly control under Y-axis flywheel fault in embodiment.

Embodiment

Below in conjunction with accompanying drawing, the technical scheme of invention is elaborated:

The semi physical platform of satellite executing mechanism on-line reorganization as shown in Figure 1, comprising: remote control computer, model emulation computing machine, spaceborne control computing machine, remote measurement computing machine, switch.

Remote control computer is formulated control strategy and is sent target control signal to spaceborne control computing machine by wireless routing.

Model emulation computing machine, gather the tach signal of flywheel, calculate the control moment acting on satellite body, then the theoretical value that draws attitude of satellite angle and angular velocity according to dynamical model, the kinematics model set up, then sends to spaceborne control computing machine by the sensor attitude measured value obtaining according to attitude sensor model by serial ports.

Spaceborne control computing machine is equipped with vxworks operating system, determine attitude of satellite angle and angular velocity according to sensor attitude measured value, resolve control law and law of distribution and obtain the working control signal of topworks according to target control signal, topworks produces attitude control moment under the effect of working control signal, and attitude of satellite angle and angular velocity transfer to remote measurement computing machine by wireless routing.VxWorks is a kind of high-performance on target machine, the embedded hard real time operating system that can reduce of operating in, and supports multiple main flow CPU, and code portability is strong.Attitude of satellite control algorithm relates to a large amount of floating-point operations, consider the hard real-time simulation requirements of satellite attitude control system, this patent proposes a kind of VxWorks real time operating system to be applied to the scheme in satellite executing mechanism on-line reorganization semi physical platform, and the real-time performance such as make full use of that VxWorks interrupt response time is short, task switching time is short improves the real-time of system.In the time that semi-physical simulation experiment is carried out in the attitude of satellite control in actuator failure situation, existing method needs to redesign control law parameter in the situation that of breaking down in topworks, workload is large, and real-time is low, and in the situation that fault is serious, even can cause the unstability of system.

Remote measurement computing machine, for dynamically showing working control signal, attitude of satellite angle and the angular velocity of topworks.

The topworks of semi-physical simulation platform can be used separately flywheel gear, also can use flywheel and magnetic torquer to jointly control.There are various configurations and mounting means in topworks, and this patent is mainly for following three kinds of modes: 1, flywheel six formal dress are installed, and on the pitching of satellite, rolling, each axle of driftage three axles, is coaxially installed with two flywheels, and one of them flywheel is as backup.2, flywheel is not arranged on pitching, rolling and three principal axis of inertia of driftage, and installs with four angle mounts or three positive oblique modes.3, flywheel three formal dress are arranged on the principal axis of inertia, and are coaxially installed with the magnetic torquer as redundancy topworks.

In conjunction with Fig. 2, satellite executing mechanism on-line reorganization control strategy of the present invention is described.For six formal dress flywheel redundant configuration and three positive one oblique or four angle mount flywheels configurations, study respectively the reconstruct control strategy based on hardware redundancy and parsing redundancy.First whether detection system breaks down, if do not break down, uses original PD control method to carry out attitude control.If break down, first extract failure message, then judge the configuration of topworks.If flywheel six formal dress configuring conditions,, in the time that a certain axle breaks down, do not consider topworks's efficiency, the backup flywheel directly switching on this axle carries out attitude control; If flywheel is three positive one oblique or four angle mount configuring conditions, in the time that a certain axle breaks down, adopt to control and distribute reconstruct control method, do not change the design of control law, according to energy optimization principle, use pseudoinverse technique design law of distribution, and consider flywheel actual output torque restricted problem, adopt the distribution amendment scheme based on kernel method, the original allocation result that pseudoinverse technique is obtained is revised, and the steering order that control law is obtained is assigned on flywheel actual used, final controlled voltage, and through DA conversion, export to each flywheel topworks; If flywheel is three formal dress mounting meanss, on three axles, be coaxially installed with magnetic torquer, according to the moment allocative decision of design, desired control moment is assigned on other the effective flywheels and three-axis magnetorquer except fault flywheel, obtain the working control signal of each topworks, after DA conversion, export to each topworks.

In conjunction with Fig. 3, implementation process of the present invention is described, Flag represents topworks's configuration zone bit, Flag=1 represents that flywheel four angle mounts or three positive tiltedly install, Flag=2 represents flywheel three formal dress and coaxial magnetic torquer is housed, Flag=3 represents flywheel six formal dress, i.e. a backup flywheel of each principal axis of inertia configuration:

(1) topworks's on-line reorganization control strategy that need to carry out physical verification is write as Matlab language program, carries out Digital Simulation;

(2) trimming operation system component, make VxWorks mirror image, bootroom, transplant vxworks operating system: on Tornado2.2 development environment, use embedded type C language compilation serial ports and network service, DA conversion, pulse hardware drive program and the attitude such as test the speed determined, attitude control, dynamics kinematics model, the application programs such as sensor model, after having debugged, be made into bootable program, be loaded into respectively in target machine PC104 (spaceborne control computing machine and model emulation computing machine), form attitude control computing machine and model emulation computer software based on multi-task scheduling,

(3) on remote control computer, use VS to set up human-computer interaction interface, complete topworks's configuration, fault is injected, and control strategy is selected, the functions such as sending controling instruction;

(4) on remote measurement computing machine, use VS and STK to set up human-computer interaction interface, complete attitude data storage, the functions such as animation and curve map demonstration;

(5) each functional module hardware is connected, power up to each operational module, and start the each program of operation;

(6)) on remote control computer, system is carried out to initialization, and select topworks's configuration, sending controling instruction;

(7) spaceborne control computing machine, according to satellite initial attitude information, sensor measurement information, flywheel fault simulation and attitude control requirement, carries out control law and law of distribution and resolves, and output order voltage is to topworks;

(8) model emulation computing machine is measured Speed of Reaction Wheels by rotating speed acquisition module, and being translated into wheel action moment, the attitude of satellite angle, the angular velocity information that sensor are recorded by kinetic model, kinematics model, environmental model, sensor model etc. pass to spaceborne control computing machine by serial communication modular;

(9) spaceborne control computing machine passes to remote measurement computing machine by the attitude information after attitude is determined by network communication module;

(10) remote measurement computing machine stores attitude angle, angular speed information into inside according in storehouse, and uses VS and STK to carry out real-time curve chart and flash demo to attitude data;

(11), under flywheel six formal dress mounting meanss, on the human-computer interaction interface of remote control computer, setting fault mode is pitch axis flywheel complete failure fault, carries out fault injection.The reconstruct control method that backs up flywheel on pitch axis is enabled in selection, by network communication mode, steering order is sent to spaceborne control computing machine, repeats above-mentioned (7) to (10);

(12), under flywheel four angle mount mounting meanss, on the human-computer interaction interface of remote control computer, setting fault mode is a certain axle flywheel fails 30%, i.e. e _i=0.3, i=1,2,3,4, select the control distribution method based on pseudoinverse technique to be reconstructed control, by network communication mode, steering order is sent to spaceborne control computing machine, repeat above-mentioned (7) to (10).

(13) flywheel three formal dress are installed, and have in coaxial mounted three-axis magnetorquer situation, on the human-computer interaction interface of remote control computer, setting fault mode is a certain axle flywheel fails 100%, select the moment allocative decision jointly controlling based on flywheel and magnetic torquer to be reconstructed control, by network communication mode, steering order is sent to spaceborne control computing machine, repeat above-mentioned (7) to (10).

The above-mentioned satellite attitude control system reconstruct control program based on revising pseudoinverse technique is carried out to Digital Simulation, the control law of checking design and the validity of distribution method, emulation initial parameter arranges as follows:

Satellite moment of inertia and flywheel are installed battle array and are taken as respectively:

$J=\left[\begin{array}{ccc}30.7& 0& 0\\ 0& 18.6& 0\\ 0& 0& 23.6\end{array}\right]\mathrm{kg}\·m^2$ $C_{4-2}=\frac{\sqrt{3}}{3}\left[\begin{array}{cccc}1& 1& -1& -1\\ 1& 1& 1& 1\\ -1& 1& 1& -1\end{array}\right]$

The control parameter of PD control law is chosen for:

K _p=diag(0.560.480.52)，K _d=diag(5.44.85.4)

Choosing satellite three-axis attitude angle and angular velocity initial value is α=[556] ^tdegree, ω=[0.50.50.5] ^tdegree/second, provide the attitude angle response curve of PD control under non-failure conditions as shown in Figure 4, be assigned to the output torque of each flywheel as shown in Figure 5.

Can find out from Fig. 4,5, in the trouble-free situation of system, the PD control law of design can ensure that system, in the time there is attitude initial deviation, converges to equilibrium state quickly, and law of distribution design based on pseudoinverse technique can be distributed to desired control moment each effect flywheel effectively.

Suppose flywheel 1 complete failure, inefficacy matrix E=diag{0,1,1,1}, 0≤e _i≤ 1, i=1,2,3,4, according to malfunction and failure situation, do not change the design of control law, carry out On-line Control moment and redistribute based on revising the distribution method of pseudoinverse technique and only use, attitude of satellite angle and angular velocity are as shown in Fig. 6 (a), Fig. 6 (b), its initial value is identical with non-failure conditions, distributes rear flywheel output torque response curve as shown in Figure 7.Visible, in the situation that a certain flywheel breaks down, use the PD control law of design and the law of distribution based on revising pseudoinverse technique, can realize the pose stabilization control of system, complete the reconstruct control under failure condition.

Flywheel and magnetic torquer combined reconstruction control program are carried out to Digital Simulation, and emulation initial parameter arranges as follows:

Initial attitude angle, angular velocity, moment of inertia and PD are identical while controlling parameter with non-fault, and orbit parameter is: semi-major axis a=642km, and eccentric ratio e=0.0001, orbit inclination i=97.3 °, 0 ° of injection point ascending node, disturbance torque model is as follows:

$M_d=\left[\begin{array}{c}1.5\×{10}^{-5}(3\cos {\mathrm{\ω}}_{0}t+1)\\ 1.5\×{10}^{-5}(1.5\sin {\mathrm{\ω}}_{0}t+3\cos {\mathrm{\ω}}_{0}t+1)\\ 1.5\×{10}^{-5}(3\sin {\mathrm{\ω}}_{0}t+1)\end{array}\right]$

For the situation of y axle generation complete failure fault, provide flywheel and magnetic torquer and jointly control result as shown in Fig. 8 (a), Fig. 8 (b), Fig. 9, Figure 10.Simulation result shows, in the situation that thering is initial attitude angle, angular velocity deviation and having external disturbance, if a certain axle of flywheel breaks down, use flywheel and the magnetic torquer combination control method of design can effectively carry out control moment distribution, realize the attitude reconstruction control under satellite executing mechanism failure condition.

Above-described embodiment has just been enumerated for six formal dress flywheel redundant configuration and three positive tiltedly or the example of the satellite executing mechanism semi physical platform of four angle mount flywheels configuration, only comprise the control method of flywheel as the semi physical platform of redundancy topworks, be coaxially installed with the control method of the semi physical platform of magnetic torquer for topworks, the checking of embodiment is only also the situation for Y-axis flywheel complete failure, but embodiment of the present invention is never confined to the example of enumerating in embodiment, every conversion that meets the embodiment of aim of the present invention or enumerated any equivalents of embodiment all falls into protection scope of the present invention.

In sum, this patent uses control distribution technique by control law and separately design of law of distribution, can make full use of system resource, simplified control system design; Break down while losing efficacy in part topworks, only need to adjust corresponding control allocative decision and need not change control algolithm and just can realize fault dynamic isolation, can make the variation minimum of system, raising system robustness; And export limited in the situation that in topworks, can be directly retrain processing controlling in allocation algorithm, reduced the complexity that controller designs.

Claims (3)

1. the semi physical platform of satellite executing mechanism on-line reorganization, is characterized in that comprising:

Remote control computer, sends target control signal to spaceborne control computing machine by switch;

Model emulation computing machine, gather the tach signal of topworks, calculate the control moment acting on satellite body, then the theoretical value that draws attitude of satellite angle and angular velocity according to dynamical model, the kinematics model set up, then sends to spaceborne control computing machine by the sensor attitude measured value obtaining according to attitude sensor model;

Spaceborne control computing machine is equipped with vxworks operating system, determine attitude of satellite angle and angular velocity according to attitude measurement value, resolve control law according to control target and obtain target control signal, resolve again the working control signal that law of distribution obtains topworks, topworks produces attitude control moment under the effect of working control signal, and attitude of satellite angle and angular velocity transfer to remote measurement computing machine by switch;

Remote measurement computing machine, for working control signal of Real time dynamic display attitude of satellite angle, angular velocity and topworks etc.

2. the semi physical platform of satellite executing mechanism on-line reorganization according to claim 1, it is characterized in that: use Visual Studio Software for Design remote control computer interface, use Visual Studio software and Satellite Tool Kit software co-design remote measurement computer interface.

3. the control method of satellite executing mechanism on-line reorganization, is characterized in that: utilize the semi physical platform of satellite executing mechanism on-line reorganization as claimed in claim 1 or 2 to obtain attitude of satellite reconstruct control program, specifically comprise the steps:

Steps A, in the time that flywheel is normally worked, utilizes and intends PD control rate u=K _pα+K _dω+ω ' J ω draws the working control signal u of flywheel, wherein, and the attitude angle that α, ω are satellite and angular speed, K _pand K _dfor ratio and differential coefficient, J is satellite moment of inertia;

Step B, in the time that a certain axle flywheel of satellite breaks down and have same axle backup flywheel, switches backup flywheel and substitutes fault flywheel, utilizes and intends PD control rate u=K _pα+K _dω+ω ' J ω draws backup flywheel working control signal u;

Step C, breaks down at a certain axle flywheel of satellite, while not having coaxially back up flywheel but have the flywheel of redundant configuration, resolves control law, law of distribution obtains each flywheel working control signal under fault:

Step C-1, uses plan PD control law ν=K according to controlling target _pα+K _dω+ω ' J ω obtains target control signal ν, and ν is control moment,

Step C-2, installs Matrix C by flywheel and obtains the relational expression of target control signal ν and working control signal u: ν=Cu,

Step C-3, by flywheel fails matrix E, determines control efficiency Matrix C _f: C _f=CE, the relational expression of combining target control signal ν and working control signal u, consider that energetic optimum uses pseudoinverse technique to control distribution, obtains law of distribution expression formula:

, u _ffor the pseudo-inverse form of flywheel working control amount under failure condition;

Step C-4, considers flywheel actual output torque restricted problem, adopts the distribution amendment scheme based on kernel method, and the original allocation result that pseudoinverse technique is obtained is revised, and obtains working control signal;

Step D, breaks down at a certain axle flywheel of satellite, and not coaxial backup flywheel but while magnetic torquer being housed on three principal axis of inertia of satellite resolves control law, law of distribution and obtain the working control signal of other effective flywheel and magnetic torquer:

Step D-1, uses plan PD control law ν=K according to controlling target _pα+K _dω+ω ' J ω obtains target control signal v,

Step D-2, according to actuator failure situation, is decomposed into by target control signal ν the controlled quentity controlled variable M that effective flywheel provides _wthe controlled quentity controlled variable M providing with magnetic torquer _m: ν=M _w+ M _m;

Step D-3, obtains according to magnetic torquer principle of work and Geomagnetic Field Model the controlled quentity controlled variable M that magnetic torquer provides _m, then determine by the expression formula of step D-2 the controlled quentity controlled variable M that effective topworks provides _w.

Images